package offer;

public class offer47 {
}
class Solution47 {
    public int maxValue(int[][] grid) {
//        定义dp[i][j]为到第i行第j列时礼物的价值
//        因为每次只能向下或者向右走，因此dp[i][j] = max(dp[i-1][j],dp[i][j-1])+grid[i][j]
//        最终走到的位置是grid[m-1][n-1]位置，初始是第一行和第一列
        int m = grid.length;
        int n = grid[0].length;
        int [][]dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i <n ; i++) {
            dp[0][i] = grid[0][i]+dp[0][i-1];
        }
        for (int i = 0; i <m ; i++) {
            dp[i][0] = grid[i][0]+dp[i-1][0];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j <n ; j++) {
                dp[i][j] = Math.max(dp[i-1][j],dp[i][j-1])+grid[i][j];

            }
        }

    return dp[m-1][n-1];
    }
}